A Discrete Multi-Tone (DMT) communication system carries information from a transmitter to a receiver over a number of tones. The tones are also commonly referred to as sub-carriers or sub-channels. The tones use a modulation method in which the available bandwidth of a communication channel, such as twisted-pair copper media, is divided into these numerous sub channels.
In the receiver, the data for each sub channel is typically extracted from the time-domain data by taking the Fourier transform of a block of samples from the multiple tone signal. Since the communication channel frequency response is not flat, the impulse response of the channel has non-zero width that causes inter-symbol interference (ISI). The ISI results from the transmitter generating a narrow well defined pulse in time, such as a rectangular shaped pulse, and by the point in time the pulse travels over the communication channel and the receiver detects and samples this pulse, the shape of the pulse has changed to a rippling wave many times the width in time of the initial pulse width. The ISI causes interdependency between successive blocks of received data such that a simple Fourier transform of each block does not correctly decode the transmitted data anymore. Thus, a first block of sampled time-domain data may slightly overlap in time with the next block of sampled time-domain data corrupting the transmitted data.
Typically, the multi-tone communication system uses filters in the receiver to retrieve the transmitted information and to minimize the ISI errors. A Time-domain Equalizer (TEQ) may employ a number of algorithms to calculate the TEQ coefficients that focus on different communication characteristics such as a signal-to-noise ratio (SNR), minimizing the inter-symbol interference, minimizing a mean-square error between a target channel and the actual channel.
Some of these algorithms try to maximize the overall signal-to-noise ratio (SNR). These algorithms tend to be very complex and not suitable for real-time implementations. A TEQ filter may use a minimum mean-square error (MMSE) algorithm to solve for TEQ filter coefficients that are based on the assumption of a known channel delay value, d to aid in retrieving the transmitted information. Other algorithms, try to minimize the inter-symbol interference (MIN-ISI) of the channel. The main objective in these algorithms is to minimize the total power of the final impulse response outside a guard period. Although these MIN-ISI algorithms are easier to implement, the resulting performance after applying these algorithms to the multiple tone signal is usually lower than applying a MMSE solution.